Robust Blind Channel Estimation for Bursty Impulsive Noise with a Constrained EM Approach

TL;DR

The paper tackles blind channel estimation in wireless links corrupted by bursty impulsive noise modeled by the Markov-Middleton process. It develops two expectation-maximization (EM) estimators for a joint BPSK-influenced hidden Markov model: a standard EM and a constrained EM that enforces shared parameters across trellis groups. The constrained EM achieves 1.5–2× faster convergence and improved estimation accuracy by leveraging the trellis structure and symmetry in state transitions, while both estimators show robustness to mismatches in Markov-Middleton parameters, albeit with slower convergence under higher CSI uncertainty. This approach enhances MAP-based detectors under bursty IN and could be extended to higher-order modulations and time-varying channels for practical deployments.

Abstract

Impulsive noise (IN) commonly generated by power devices can severely degrade the performance of high sensitivity wireless receivers. Accurate channel state information (CSI) knowledge is essential for designing optimal maximum a posteriori detectors. This paper examines blind channel estimation methods based on the expectation-maximization (EM) algorithm tailored for scenarios impacted by bursty IN, which can be described by the Markov-Middleton model. We propose a constrained EM algorithm that exploits the trellis structure of the IN model and the transmitted binary phase shift keying (BPSK) symbols. By enforcing shared variance among specific trellis states and symmetry in the transition matrix, the proposed constrained EM algorithm adapted for the bursty IN channel has an almost two times faster convergence rate and better estimation performance than the standard EM approach. We comprehensively evaluate the robustness of both standard and constrained EM estimators under different types of CSI uncertainties. The results indicate that the final estimations of both EM estimators are robust enough to mismatch Markov-Middleton model parameters. However, as the level of CSI uncertainty increases, the convergence rate decreases.

Figures (2)

• Figure 1: Noise realization from a $2$-state Markov-Middleton model ($W=2$) with $\sigma^2_{w_0}=1$ for $A=0.1$ and $A=0.3$, $\Lambda=1$ and $\Lambda=10$, and $r=0$ and $r=0.9$. The orange vertical bar denotes the index $j$ of the state realizations $w_t = j$ for generating the corresponding noise samples.
• Figure 2: Trellis section of a BPSK transmission over a 2-state ($W=2$) IN model, where each state $s_t=j$ denote a single Gaussian component $\mathcal{N}(\mu_{s_j}, \sigma^2_{s_j})$. The state transitions are driven by ($x_t$, $w_{t-1}$, $w_{t}$) with probabilities $P_{s_{ij}}$. We use the same color to indicate metrics that share identical values.